Energy derivatives in real-space diffusion Monte Carlo

TL;DR

This paper introduces unbiased, finite-variance estimators for energy derivatives in real-space diffusion Monte Carlo, addressing divergence issues through regularization techniques and demonstrating their effectiveness with a simplified model.

Contribution

It provides the first unbiased, finite-variance estimators for energy derivatives in real-space diffusion Monte Carlo, incorporating novel regularization methods.

Findings

Successfully regularized divergence in energy derivative estimators.

Demonstrated the approach with a particle-in-a-box toy model.

Ensured consistency of derivatives with energy dependence on parameters.

Abstract

We present unbiased, finite--variance estimators of energy derivatives for real--space diffusion Monte Carlo calculations within the fixed--node approximation. The derivative $d_\lambda E$ is fully consistent with the dependence $E(\lambda)$ of the energy computed with the same time step. We address the issue of the divergent variance of derivatives related to variations of the nodes of the wave function, both by using a regularization for wave function parameter gradients recently proposed in variational Monte Carlo, and by introducing a regularization based on a coordinate transformation. The essence of the divergent variance problem is distilled into a particle-in-a-box toy model, where we demonstrate the algorithm.